Notes Chapter 7 Bivariate Data

Relationships between two (or more) variables. The response variable measures an outcome of a study. The explanatory variable attempts to explain the observed outcomes.

When we gather data, we may have in mind which variables are which. There may also not be explanatory & response variables if our data does not suggest “causation”.

Displaying the Variables The most effective way to display a relation between two quantitative variables is a scatterplot. –It shows the relationship between two quantitative variables measure on the same individual. –Each individual in the data appears as the point in the plot fixed by both values. –Always plot the explanatory variable (if there is one) on the horizontal (the x axis) of a scatterplot.

Interpret a Scatterplot First, look for an overall pattern to include: –1) direction (positive, negative) D –2) form (linear, exponential, quadratic) S –3) strength (correlation, r) S –4) deviations from the pattern (outliers) U SUDS!!

Remember on outlier in any graph of data is an individual observation that falls outside the overall pattern of the graph. There is no outlier test for bivariate data. It is a matter of…hey, does that point look out of place?

Categorical variables can be added to scatterplots by changing the symbols in the plot. (See P. 199 for examples) Visual inspection is often not a good judge of how strong a linear relationship is. Changing the plotting scales or the amount of white space around a cloud of points can be deceptive. So….

Facts about Correlation: 1) positive r – positive association (positive slope) negative r – negative association (negative slope) 2) r must fall between –1 and 1 inclusive. 3) r values close to –1 or 1 indicate that the points lie close to a straight line. 4) r values close to 0 indicate a weak linear relationship. 5) r values of –1 or 1 indicate a perfect linear relationship. 6) correlation only measures the strength in linear relationships (not curves). 7) correlation can be strongly affected by extreme values (outliers).